# Sample size for Attribute data – Rule of Thumb

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- This topic has 5 replies, 4 voices, and was last updated 14 years, 12 months ago by Jürgen De Cock.

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- February 24, 2005 at 12:30 am #38536
Can anyone explain the following rule of thumb for estimating a minimum sample size for attribute data as taught to us by a Master Black Belt?:

np > 5

n = sample size

p = proportion defective

So if you wanted to estimate a sample size and you knew that you had a 1% defect rate (p = 0.01), you’d need to take a minimum of sample size of 500. I can’t work out where this rule of thumb comes from, what the assumed confidence level is, etc.0February 24, 2005 at 5:01 am #115300I’m not sure why *your* MBB likes this rule of thumb ;-) but I can come to a couple of conclusions why this would be a good number. When np > 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations. 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations. 5, then the normal approximation is pretty good, which is a useful thing for all sorts of calculations.Another feature is of this rule of thumb is related to the standard deviation and confidence intervals. Whether you officially have a Poisson distribution or a binomial distribution, the standard deviation will be pretty close to np^0.5 = 5^0.5 = 2.2. The 95% confindence interval would run from roughly 5 +/- 4.4, which does not include 0. So if you get 0 defect, you can be pretty sure it is better than 1%.

On the other hand, getting double the expected defect rate is evidence of slipping performance.On the other hand, if np = 4, the 95% confidence interval runs basically from 0 to 8, so even getting zero defects is not strong evidence of improvement.

And getting double the defects is still not a strong sign of bad performance.

Tim F0February 24, 2005 at 5:28 am #115302Go pick up a copy of Juran’s QC Handbook and fire your MBB.

0February 24, 2005 at 6:21 am #115307Hmmm… I’ve got lots of “QC Handbook” type guides and textbooks. Couldn’t find any explanations in any of these. Looked up the web using Google, couldn’t find any explanation, searched isixsigma – couldn’t find any explanation. Must be some somewhere though…

:-)0February 24, 2005 at 6:46 am #115310Go find the chapter on statistical methods in Juran’s handbook and find the info on when it is appropriate to approximate one distribution with another.

0February 24, 2005 at 12:10 pm #115318

Jürgen De CockParticipant@Jürgen-De-Cock**Include @Jürgen-De-Cock in your post and this person will**

be notified via email.The following book explains (next to a lo of other stuff) how to calculate sample sizes.

Implementing Six Sigma by Forrest W. BreyfogleIII.ISBN 0-471-29659-7 (second edition) I know know there is a third edition.

page 310 – 320 handels about it.

generally spoken a verry good book.0 - AuthorPosts

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